Virginia you are right the city attorney is a totally different think than the District Attorney. The city attorney advises the city on legal matters, and goes to court on behalf of the city.
I am not sure how New Troy is set up (OK, since it does not exist, and is sort of New York, except I think in this espisode they mention New York, and the map in the pilot makes it look at least to me like Metropolis is in Pennsylvania, so we just know it is not New Jersey <from what they say in "Twas the Night Before Mxymass"> so you probably have multiple options on how the DA works. In Michigan we don't even call the state(ish) prosecutors DAs, we call them County Prosecutors, because they are elected by county. There are federal district attorney's (I think we have at two in Michigan) who handle federal cases, but in most other states they also have state DAs who are elected by "district" that may or may not correspond to anything.
That said, being the DA would probably be a step up from being the city attornye (especially if Chung is not the city attorney, but just on the staff), so I could imagine the city attorney running for the more powerful position of DA. Federal DAs are not elected, but appointed by the president with the advice and consent of the senate, and I don;t think any state has more than four (each of which covers a specific part of the state). New York City though is split between two US District Attorney's though, although both cover more than the city.
